Method for operating continuous casting machine

ABSTRACT

A primary object of this invention is to provide a method for operating a continuous casting machine with which a mold can oscillate with a predetermined oscillation waveform since the start of operation of an oscillator. This invention is a method for operating a continuous casting machine, the method comprising: withdrawing a slab from a mold while vertically oscillating the mold with an oscillation waveform represented by the following formula (1) by selecting a value of φ according to a value of b so that the following formula (1) satisfies r(0)=0: 
         r ( t )=( S/ 2){sin(ω t +φ)+ b  cos 2(ω t +φ)+ b}   ( 1 )
 
     where r(t): displacement of the mold (mm), S: vibration stroke of the mold S (mm), ω: angular velocity (=2πf) (rad/s), f: oscillation frequency of the mold (Hz), t: time(s), φ: initial phase (°), and b: non-sine coefficient (0&lt;b≦0.25).

TECHNICAL FIELD

This invention relates to a method for operating a continuous castingmachine used for continuous casting, and specifically, related to amethod for operating a continuous casting machine of oscillating a mold.

BACKGROUND ART

Continuous casting of steel is carried out in such a way that: moltensteel is poured from a ladle via a tundish into a mold; and after asolidified shell forms in the mold, a slab including an unsolidifiedarea is withdrawn downward underneath the mold. When a continuouscasting machine is operated, especially when molten steel is cast athigh speed, there is a case where part of the solidified shell isconstrained from being withdrawn by stick on an inner wall of the moldand this constrained part functions as a hindrance to formation of anormal solidified shell. In this case, not only various faults but alsobreakout might occur in products.

Conventionally, powder to be put into molten steel in a mold is selectedto deal with this problem. Molten powder floats and spreads over thesurface of the molten steel, is supplied to a space between the mold andthe solidified shell, and functions as a lubricant reducing frictionalforce between them. Whereby, stick of the solidified shell on the innerwall of the mold can be suppressed in some degree.

However, in recent years, operation of continuous casting has beenapplied for various kinds of steel grades, and carried out under variouscasting conditions. Therefore, there is a limit if physical propertiesof powder are changed to deal with such various situations. Thus, such amethod is tried that a mold is oscillated at the same time when powderis put. Proper oscillation of the mold makes it possible to suppressstick in the mold.

Patent Literature 1 discloses applying, to a casting mold, verticaloscillation, having a deviated sine waveform that is deviated from asine waveform. Patent Literature 1 gives the following formula (X) as aspecific deviated sine waveform:

Z=a ₁sin 2πft+a ₂sin 4πft+a ₃sin 6πft   (X)

where Z is displacement of the mold (mm), a₁, a₂, a₃, . . . areamplitude (mm), f is oscillation frequency of the mold (cycles/s) and tis time(s).

According to Patent Literature 1, oscillation having the waveformrepresented by the above formula (X) is controlled so that:

-   -   (i) the maximum descending speed of the mold during negative        strip time is fast;    -   (ii) the maximum ascending speed of the mold during positive        strip time is slow;    -   (iii) the negative strip time is short; and    -   (iv) the positive strip time is long,        compared to the case where the oscillation waveform is a sine        wave.

The negative strip time is time when the descending speed of the mold isfaster than the withdrawal rate of an unsolidified slab. The positivestrip time is time when the speed of the mold is slower than thewithdrawal rate of the unsolidified slab. According to Patent Literature1, meeting the requirements of the above (i) to (iv) makes it possibleto increase the inflow of molten powder into a space between the moldand the solidified shell and to suppress occurrence of breakout.

However, in the method of Patent Literature 1, the movement of the moldsuddenly changes from the ascent to the descent upon the oscillation ofthe mold. At this time, molten powder adhered in the vicinity ofmeniscus in the mold and unmolten powder are involved in molten steel.Whereby, the surface quality of a slab deteriorates and/or troubles onthe operation occur depending on a type of powder used.

Conventionally, an oscillator including an electric motor and aneccentric cam is used for oscillating a mold. A desired oscillationwaveform is obtained according to a shape of an eccentric cam. In thiscase, an eccentric cam corresponding to an oscillation waveform has tobe prepared for changing the oscillation waveform. In recent years, anelectro-hydraulic oscillator has been used for oscillating a mold, whichhas made it easy to change parameters when a mold is oscillated withcomplex waveforms as disclosed in Patent Literature 1 and PatentLiterature 2 below.

Patent Literature 2 discloses the method for operating a continuouscasting machine comprising vertically vibrating a mold with the waveformexpressed by the formula (Y) below:

Z=A(sin 2πft+b cos 4πft+c)   (Y)

where Z is displacement of the mold (mm), A is ½ of a vibration stroke Sof the mold (mm), b is strain constant, c is strain constant, f isvibration frequency of the mold (Hz/60) and t is time (s).

According to Patent Literature 2, employment of such a vibrationwaveform makes it possible that abrupt change in the mold from an ascentto a descent does not occur, and molten and unmolten powder are notinvolved in molten steel.

When such a vibration waveform is employed, a neutral position of theoscillation shifts to either upper or lower side. In this case, symmetryof the oscillation is secured in vertical type continuous casting, inwhich a path where an unsolidified slab travels in a mold is in aperpendicular direction. On the contrary, in curved type continuouscasting, in which a path where an unsolidified slab travels in a moldcurves, symmetry of oscillation is broken, and such a problem tends tobe arose like poor lubrication in the mold and involvement of powderinto molten steel.

If the above vibration waveform in Patent Literature 2 is employed, thedisplacement Z at the time t=0 is not 0 but SC/2. In this case, a moldcannot oscillate with a predetermined oscillation waveform at the startof operation of an oscillator that oscillates the mold, and the mold isdisplaced step by step as time passes, for example. This disables adummy bar, which seals an opening in the bottom side of the mold at thestart of casting, to seal an opening enough, and molten steel might leakout of the mold.

CITATION LIST Patent Literature

Patent Literature 1: Japanese Examined Patent Application PublicationNo. H4-79744

Patent Literature 2: Japanese Patent No. 3651447

SUMMARY OF INVENTION Technical Problem

An object of this invention is to provide a method for operating acontinuous casting machine with which poor lubrication and involvementof powder into molten steel due to the above problems of the prior arts,especially due to the shift of a neutral position in curved typecontinuous castingcan be prevented.

Another object of this invention is to provide a method for operating acontinuous casting machine with which troubles at the initial stage ofcasting (like seal leakage) can be prevented, and with which a mold canoscillate with a predetermined oscillation waveform since the start ofoperation of an oscillator.

Solution to Problem

The essentials of this invention include the following method foroperating a continuous casting machine:

A method for operating a continuous casting machine where a slab iswithdrawn from a mold for continuous casting while the mold isoscillated in a vertical direction, the method comprising:

oscillating the mold so as to satisfy the following formula (2) with anoscillation waveform represented by the following formula (1):

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 1} \right\rbrack & \; \\{{r(t)} = {\left( {S/2} \right)\left\{ {{\sin \left( {{\omega \; t} + \phi} \right)} + {b\; \cos \; 2\left( {{\omega \; t} + \phi} \right)} + b} \right\}}} & (1) \\{\varphi = {{\pm \tan^{- 1}}\left\{ {\frac{1}{\sqrt{2}}\sqrt{\left( {1 + {16b^{2}}} \right) - 1}} \right\}}} & (2)\end{matrix}$

wherein r(t) is displacement of the mold (mm),

S is an oscillation stroke of the mold S (mm),

ω is angular velocity (=2πf) (rad/s),

f is oscillation frequency of the mold (Hz),

t is time (s),

cp is the initial phase (°), and

b is a non-sine coefficient (0<b≦0.25).

Advantageous Effects of Invention

According to the operation method of this invention, a mold oscillateswith an oscillation waveform represented by the above formula (1). Aneutral position does not shift with the oscillation waveformrepresented by the above formula (1) in curved type continuous casting.Therefore, poor lubrication and involvement of powder into molten steelcan be prevented.

Satisfaction of the above formula (2) makes the displacement of a mold 0when r(0)=0, that is, at the start of operation of an oscillator.Therefore, the mold can oscillate with a predetermined oscillationwaveform since the start of operation of the oscillator, and thus,troubles at the initial stage of casting can be prevented.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a cross sectional view showing an example of the structure ofa continuous casting machine to which the operation method of thisinvention can be applied.

FIG. 2 shows oscillation waveforms when b=0.40 and φe=33.66 (oscillationwaveforms of Reference Example).

FIG. 3 shows oscillation waveforms when b=0.15 and φ=16.08 in thisinvention.

FIG. 4 shows oscillation waveforms when b=0.20 and φ=20.535 in thisinvention.

FIG. 5 shows oscillation waveforms when b=0.25 and φ=24.46 in thisinvention.

FIG. 6 shows the maximum frictional force per oscillation waveform.

DESCRIPTION OF EMBODIMENTS

FIG. 1 is a cross sectional view showing an example of the structure ofa continuous casting machine to which the operation method of thisinvention can be applied. A tundish 1 is stocked with molten steel 6supplied from a ladle not shown. A tubular mold 3 having an opening ateach top and bottom thereof is arranged below the tundish 1. The moltensteel 6 is poured from the tundish 1 via the immerged nozzle 2 into themold 3 through the opening at the top of the mold 3.

An oscillator 20 is connected to the mold 3. The oscillator 20 iselectro-hydraulic, and can vertically oscillate the mold 3. Theoscillator 20 includes a controlling part. Parameters of waveforms canbe inputted to the controlling part. The oscillator 20 can generateoscillation having various waveforms based on inputted parameters.Oscillation having a waveform generated by the way described above isapplied to the mold 3 during continuous casting.

Powder is put into the molten steel 6 in the mold 3. Powder melts withheat of the molten steel 6, to become molten powder, and spreads overthe surface of the molten steel 6 in the mold 3. In the molten steel 6,a contact portion with or a portion in the vicinity of a part facing themold 3 are cooled, solidified, to be a tubular solidified shell 7. Themolten powder is supplied to a space between the mold 3 and thesolidified shell 7. Whereby, frictional force between the mold 3 and thesolidified shell 7 is decreased.

The inside of the solidified shell 7 is filled with the molten steel 6.The molten steel 6 is not completely solidified by passing through themold 3, to be an unsolidified slab including an unsolidified part. Theunsolidified slab is cooled by cooling water jetted out of secondarycooling spray nozzles arranged below the mold 3, which are not shown.Whereby, the solidified shell 7 enlarges.

As being supported by foot rolls 4 arranged right under the mold 3 andplural of roller aprons 5 arranged in the downstream side of the footrolls 4 in the direction where the unsolidified slab travels(hereinafter just referred to as “downstream side”), the unsolidifiedslab is withdrawn by pinch rolls 8 arranged in the downstream side ofthe roller aprons 5. The unsolidified slab is reduced by reduction rolls9 arranged in the downstream side of the pinch rolls 8, to be a slabthat does not substantially contain any unsolidified part.

As described above, in the method for operating a continuous castingmachine of this invention, the mold oscillates with the oscillationwaveform represented by the formula (1). While the waveform of theformula (X) in the prior art is a composite waveform that is thecombination of only sine waves of different cycles, the waveform of theformula (1) is a composite waveform of a sine wave and a cosine wave.Further, the formula (1) is significantly different from the formula (X)in introduction of the initial phase φ and r(0)=0.

In the formula (1), let φ=0. The displacement of the mold r(t) is themaximum value (S/2) when ωt=π/2, and is the minimum value (−S/2) whenωt=− /2. The maximum value and the minimum value of the displacement ofthe mold r(t) do not depend on the initial phase φ. Thus, a neutralposition does not shift in the oscillation waveform represented by theformula (1). Therefore, poor lubrication and involvement of powder intothe molten steel can be prevented not only in vertical type continuouscasting but also curved type continuous casting.

The formula (3) below has to be satisfied in order for the displacementof the mold to be 0 when the time t=0. The formula (3) below is obtainedby substituting 0 for t, to be r(0)=0 in the formula (1):

0=sin φ+b cos 2φ+b   (3)

Using the formula of a trigonometric function, cos 2φ=1−2 sin²φ, theformula (3) can be rewritten into the formula (4) below:

2 bsin²φ−sin φ−2b=0(b>0)   (4)

Since |sin φ|≦1, the following formula (5) is obtained if sin φ is madeto be the subject of the formula (4):

sin φ={1−(1+16b ²)^(1/2)}/4b   (5)

If φ is made to be the subject of the formula (5) using the formulae ofa trigonometric function, tan φ=sin φ/cos φ and cos φ±(1−sin₂φ)^(1/2),(2) is obtained.

That is, satisfaction of the formula (2) makes the displacement of themold r(0) 0 when the time t=0. Therefore, it becomes possible tooscillate the mold with a predetermined oscillation waveform since thestart of operation of the oscillator that oscillates the mold, and towell seal the opening of the mold with a dummy bar.

Two values of φ are determined by the formula (2). If a direction of themovement of the mold at the start of oscillation is upward, φ thatsatisfies cos φ>0 may be employed since dr(0)/dt>0.

A non-sine coefficient b is any value within the range of 0<b<0.25.

“b” is a coefficient of cos 2(107 t+φ) in the term of b cos 2(ω+φ), anddetermines magnitude of the term of b cos 2(ωt+φ) to the term of sin(107t+φ). In a case of 0.25<b, the term of b cos 2(ωt+φ) is too largecompared to the term of sin(ωt +φ), which arises a problem that the molddescends when ω+φ=π(½+2n) (n is 0 or a positive integer), where the moldshould ascend most. Thus, b≦0.25. For your reference, FIG. 2 shows thewaveforms when b=0.4 and the initial phase φ=33.66°. As shown in FIG. 2,in the case of b=0.4 that satisfies 0.25<b, the mold descends whenωt+φ=π(½+2n) (n is 0 or a positive integer), where the mold shouldascend most. Therefore, in this invention, b≦0.25.

On the other hand, when b is 0, the waveform of the displacement of themold r(t) shows simple harmonic motion. In this case, compared with thecase of 0<b, the inflow of the molten powder into a space between themold and the solidified shell cannot be increased. Thus, in thisinvention, 0<b. Preferably 0.15≦b in this invention in order to increasethe inflow of the molten powder enough compared with the case of thesimple harmonic motion.

Table 1 shows values of the initial phase (p determined by the formula(2) in each case where the non-sine coefficient b is 0.15, 0.20 and0.25. It makes r(0)=0 possible that a value of the initial phase φ thatsatisfies the formula (2) is employed according to a value of thenon-sine coefficient b.

TABLE 1 Non-sine Coefficient (b) 0.15 0.20 0.25 Initial Phase (φ) 16.0820.535 24.46

FIGS. 3 to 5 show waveforms based on the formula (1) (relation betweenthe time t and the displacement of the mold r(t)) when the combinationshown in Table 1, that is, (b=0.15, φ=16.08), (b=0.20, φ=20.535),(b=0.25, φ=24.46) are employed as values of the non-sine coefficient band the initial phase φ.

In FIGS. 3 to 5, the part of sin(ωt+φ) in the formula (1) is shown as aprimary waveform, the part of b cos 2(ω+φ) therein is shown as asecondary waveform, and r(t) therein is shown as a composite waveform,where S=4 mm and ω=2πrad/s.

In each composite waveform shown in FIGS. 3 to 5, change in movementspeed in the vicinity of the maximum displacement (peak) is small, andthat in the vicinity of the minimum displacement (bottom) is largecompared to the case where an oscillation waveform is a sine wave. Asthe non-sine coefficient b is larger, time when the change in movementspeed in the vicinity of the maximum displacement is small is longer.The movement speed of the mold (ascending speed and descending speed) isfast during the time between the vicinity of the minimum displacementand the vicinity of the maximum displacement, compared to the case wherean oscillation waveform is a sine wave.

The fast descending speed of the mold makes the amount of the moltenpowder that is pushed (pumped) into a space between the mold and thesolidified shell increase. The fast ascending speed of the mold makesthe powder possible to reach closer area to the inner wall surface ofthe mold (makes it possible to broaden the flow path of the powder). Thelong time when change in the movement speed of the mold in the vicinityof the maximum displacement is small makes it possible to keep the statewhere the flow path of the powder broadens long. Therefore, thelubricity between the mold and the solidified shell can be improved byvertical oscillation of the mold with any composite waveform shown inFIGS. 3 to 5.

The displacement of the mold in the case of t=0 is at the middleposition between the maximum displacement (2 mm) and the minimumdisplacement (−2 mm), that is, at a neutral position in every compositewaveform shown in FIGS. 3 to 5. Whereby, troubles at the initial stageof casting such as seal leakage can be prevented. The neutral positiondoes not shift. So, the effect of suppressing poor lubrication in themold and involvement of the powder into the molten steel can be stablybrought about.

While the lubricity between the mold and the solidified shell can bemore improved as the non-sine coefficient b is larger, some kinds ofphysical properties of the powder cause the molten powder to be easilyinvolved into the molten steel. In view of the above, preferably, aproper value of the non-sine coefficient b is employed according tophysical properties of powder, or powder of proper physical propertiesis employed correspondingly to the value of the non-sine coefficient b.For example, when the value of the non-sine coefficient b is large,involvement of the molten powder into the molten steel can be suppressedefficiently if powder of a high solidification point, and in a moltenstate, of high viscosity is employed.

Difference in performance of the lubricity of powder of differentoscillation waveforms were examined. As oscillation waveforms, a sinewave, the waveform shown in FIG. 3 (b=0.15) and the waveform shown inFIG. 5 (b=0.25) were used. Continuous casting was carried out as a moldoscillated vertically with each waveform using an electro-hydraulicoscillator. The powder of the same properties (solidification point:1154° C., viscosity of the molten powder at 1300° C.: 0.14 Pa·s) wasused for every case where the mold oscillated with the above mentionedoscillation waveform. Load when the mold oscillated, which was themaximum load during the time when the mold ascended (hereinafter simplyreferred to as “max load”), was measured by the above electro-hydraulicoscillator.

The performance of the lubricity was evaluated by the maximum frictional1.5 force. The maximum frictional force F was represented by

F=(L1−L2)/S,

where L1is the max load at the casting (when the molten steel existed inthe mold);

L2 is the max load when the casting was not carried out (when the moltensteel did not exist in the mold; and

S is an area of a part that touched or faced the molten steel in theinner face of the mold.

FIG. 6 shows the maximum frictional force for the oscillation waveforms.The maximum frictional force is small in the case the waveforms shown inFIGS. 3 and 5 were used as oscillation waveforms compared to the casewhere the sine wave is used. That is, the performance of the lubricityof the powder between the mold and the solidified shell was high in thecase where the waveform of the formula (1) (b=0.15, 0.25) compared tothe case where the sine wave was used. The performance of the lubricitywas higher in the case of b=0.25 than the case of b=0.15.

REFERENCE SIGNS LIST

-   3 . . . mold-   20 . . . oscillator

1. A method for operating a continuous casting machine where a slab iswithdrawn from a mold for continuous casting while the mold isoscillated in a vertical direction, the method comprising: oscillatingthe mold so as to satisfy the following formula (2) with an oscillationwaveform represented by the following formula (1): $\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 1} \right\rbrack & \; \\{{r(t)} = {\left( {S/2} \right)\left\{ {{\sin \left( {{\omega \; t} + \phi} \right)} + {b\; \cos \; 2\left( {{\omega \; t} + \phi} \right)} + b} \right\}}} & (1) \\{\varphi = {{\pm \tan^{- 1}}\left\{ {\frac{1}{\sqrt{2}}\sqrt{\left( {1 + {16b^{2}}} \right) - 1}} \right\}}} & (2)\end{matrix}$ wherein r(t) is displacement of the mold (mm), S is anoscillation stroke of the mold S (mm), ω is angular velocity (=2πf)(rad/s), f is oscillation frequency of the mold (Hz), t is time (s), φis the initial phase(°), and b is a non-sine coefficient (0<b≦0.25). 2.The method for operating a continuous casting machine according to claim1, wherein 0.15≦b.